To extract a damaged ceramic or quarry tile, first hammer the surface to break the tile up into small pieces, working from the centre outwards. Using a narrow cold chisel, chip away these fragments and chisel out the old adhesive. Finally, brush away all traces of dust from the cavity.
Lay the replacement tile within the hole to check that it fits. Then remove the tile, spread adhesive on the back and press it home. Fitting it flush with the adjacent tiles. Clean any excess adhesive from the joints before it sets. Leave to dry. Grout a day later.